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Introduction to Coulomb Blockade and Single Electron Devices

voltage driven capacitor
Figure 1.

In a circuit formed by a capacitor driven by a voltage source, (see fig. 1) the current flow is zero. However if the plates of the capacitor are separated by a very small distance, then electrons can tunnel across the gap. In that tunnel junction, (see fig. 2) the current-voltage (I-V)  characteristic is linear at small applied voltages, and the voltage on the junction will feature some noise. If the tunnel junction is driven by a current source, the I-V is still linear with the slope determined by the resistance of the tunnel junction.

large tunnel junction
Figure 2.

Now if the capacitance of the tunnel junction is extremely small ( <<  1 fF), and the temperature is low, then a remarkably new feature emerges when the junction is driven by a small current from a current source. As shown in figure 3, the junction voltage oscillates.   In addition, the averaged I-V  is now non-linear and  features a threshold voltage.  The oscillation is a consequence of regulated single electron tunneling. Both the junction voltage oscillation, and the threshold in the I-V are manifestations of the coulomb blockade effect.

current-voltage characteristics

Figure 3.

 The term coulomb blockade is another way to state a salient attribute of tunneling:  tunneling cannot lead to an increase in the coulomb energy of a system; and that enables classical control of a quantum process. In the above case of a single junction, the change in the potential energy of the capacitor (Q*Q/(2c))  is less than or equal to zero only when the magnitude of charge on the junction is larger than half the charge of an electron (abs(Q) > e/2 ).   Hence at the start of a cycle, the current source charges the capacitor, then when the charge reaches e/2,  a single  electron tunnels, the voltage drops, then the junction is again recharged; then the process repeats. The threshold feature in the time-averaged I-V can be used to design single electron devices.